project G

1 INTRODUCTION

Slope stability is one of the important geotechnical engineering

applications. Geotechnical engineers aim is to achieve optimum design

with minimum cost using the readily available material. This research was

performed to find alternative solutions for soil slope stability application,

specifically slope of soil embankment. Various options for reinforcement

of retaining structure will be studied. Specifically reinforced earthen

retaining walls will be considered. The suitability of using Geosynthetics

products in retaining structure application will be studied in detailed.

2 BACKGROUND AND PREVIOUS WORK

Since most of the different constructions and structures are deal with soil,

soil must be controlled and perform to be provided to service that

constructions. Since most of these constructions are required to attend to

construct with earth retaining structure. This is which known soil stability.

2.1 METHODS OF SOIL STABILITY

Soil stability is a term used widely in civil engineering applications.

Stability could be gained simply by using a steeled mesh known as gabion

mesh. Another common method is widely used which work to provide

lateral support is known as conventional retaining wall. But most of field

applications now required a more effective stability. This could be applied

by using a specific manufactured material to reinforce the soil. This will

provide a mechanical process known as soil reinforcement. This

mechanical process helps the instability soil to against itself. Soil is

reinforced with polymer materials known as Geosynthetics. This study

evaluates the alternative of the conventional retaining wall structures by

using Geosynthetics reinforced structures known as the Mechanically

Stabilized Earth walls (MSEW).

2.2 SOIL REINFORCEMENT WITH GEOSYNTHETICS

Reinforced soil technique for reinstatement of failed slop using

Geosynthetics product is used as alternative of methods stated above.

Soil reinforcement based on controlling the load applied occurs due to soil

weight and other external loads may be considered. Reinforcement with

Geosynthetics material transfers the vertical load to tensile load applied

for a calculated natural compacted soil layer thickness to a specific

Geosynthetics material which fabricated for that suppose. This process

Lead that Load to developed at very low strains by the soil.

2.3 Geosynthetics

Geosynthetics is the term used to describe a range of generally polymeric

products used to solve civil engineering problems. Geosynthetics provide

long-lasting reinforcement, and to increase soil stability. When placed in

the direction of soil deformation, Reinforcement Geosynthetics generate

tensile forces to carry tensile stress. The high stiffness of the

Reinforcement Geosynthetics prevents excessive deformation in the soil.

Bonds develop between the soil and Reinforcement Geosynthetics

efficiently transferring stress into the surrounding soil through

interlocking, friction, and end bearing resistance.

The term is generally regarded to encompass seven main product

categories: Geotextile, Geogrid, Geonet, Geomembrane, Geosynthetics

clay liners, Geofoam and Geocomposite. The polymeric nature of the

products makes them suitable for use in the ground where high levels of

durability are required. Properly formulated, however, they can also be

used in exposed applications. Geosynthetics are available in a wide range

of forms and materials, each to suit a slightly different end use. These

products have a wide range of applications and are currently used in many

civil engineering problems. The following paragraphs describe each type

of Geosynthetics material and typical use in engineering applications.

2.3.1 Geotextile

Geotextile is a permeable Geosynthetics made of textile materials. When

used in association with soil, have the ability to separate, filter, reinforce,

protect, or drain Geotextile are made from polypropylene or polyester

material.

2.3.2 Geogrid

Geogrid are synthetics planar structure primarily used for reinforcement

applications. Geogrid used as reinforcement material to add tensile

strength to soil matrix, so providing more stability structure. It's also used

as separated material when it used to separate fine-grained sub grade in

road way. Geogrid formed by a regular network of tensile elements with

apertures of sufficient size to interlock with surrounding fill material. It's

important to note that most Geogrids are manufactured to function

uniaxially although the present of the biaxial Geogrids and that well affect

the method manufactory. Geogrids have higher stiffness and strength than

most Geotextiles. Geogrid also used to tensile reinforce steep slopes,

retaining structures, and embankments constructed over soft foundation.

2.3.3 Geonet

Genets are formed by continuous extrusion of parallel sets of polymeric

ribs at acute angles to one another. When the ribs are opened, relatively

large apertures are formed into a netlike configuration. Their design

function is completely within the in-plane drainage area where they are

used to convey all types of liquids.

2.3.4 Geomembrance

Geomembranes are low permeability Geosynthetics used as fluid barriers.

Geomembranes are a good material used in landfill sites for the

containment of hazardous or municipal wastes and their leachates. In

many of these applications Geomembranes are employed with Geotextile

or mesh underlines which reinforce or protect the more flexible

Geomembranes whilst also acting as an escape route for gases and

leachates generated in certain wastes.

2.3.5 Geosynthetics clay liners

Geosynthetic clay liner (GCL) is a woven fabric like material primarily

used for the lining of landfills. It is a kind of Geomembranes and which

Geosynthetics incorporates a betonies or other clay, which has a very low

hydraulic conductivity. The resulting lower permeability slows the rate of

seepage out of the landfill.

2.3.6 Geofoam

Geofoam is made of expended polystyrene (PES). It’s used as a light

weight fill under a road sub-grid. Belt over a low load bearing soil.

Geofoam also has also found application for vibration damping, gas

venting and soil stabilization.

2.3.7 Geocomposite

Geocomposites is a combination made from two or more Geosynthetics

by bonding together (mostly Geomembranes/Geonet and Geotextile) for

specie applications in drainage, filtration, fluid transmission, erosion

control.

Geotextile and related products can combined with Geomembranes

material and other synthetics, to complement the best attributes of each

material. The most attributes should consider is drainage with a specific

volumetric flow. The hydraulic properties are a major consideration in

design. The flow rate obtained from the tests is reduced using reduction

factors considering soil clogging and blinding, creep reduction of void

space, intrusion of adjacent materials into Geotextile voids, chemical

clogging, and biological clogging. But sometime large capacity is

required for design.

In this research we will spot light on georgic and Geocomposites

Geosynthetics materials to be consider for our studying.

3 Basic performance properties of Geogrid, Geotextile and Geonet

Geogrid:

Geogrid used in past in first appearance which was made of high density

of polyethylene (HDPE) and sometime made of PET which designed to

carry a load not exceed 250 kN per unit length and which widely used in

side slope reinforcement. Now, Geogrid is manufactured to be stronger

.Geogrid classified related to variety of stiffness which includes:

1. Stiff Geogrid, mostly HDPE with a monolithic mesh structure

2. Flexible Geogrid, mostly PET with PVC or acrylic coating with

mechanically connected longitudinal and transverse elements.

Geogrid fabrics on two functions related to suppose used uniaxially and

biaxial. In manufacturing uniaxial Geogrids, circular holes are punched on

the polymer sheet, which is subsequently drawn to improve the

mechanical properties. For biaxial Geogrids, square holes are made on the

polymer sheet, which is then drawn longitudinally and transversely.

Uniaxial Geogrid Biaxial Geogrid

Figure 1 Uniaxial and biaxial Geogrids

Geonet:

All Geonets are made of polyethylene. Geonet are made b Extrusion

corresponding sets of polymeric ribs at acute angles to one another. The

ribs are opened, relatively large apertures are shaped into a netlike pattern.

The only other materials in Geonets are carbon black and a processing

package. The specific gravity of most Geonets is in the range of 0.935 to

0.942.

Geotextile:

Geotextile are made primly of fibers or yarns. Thus these product could

be indentify by polymer were used .high strength polymer grids are made

from extruded sheet of polymer (polypropheline or polyethylene) where

first punched with a regular patterns of holes. Then sheet is stretched in

controlled temperature. Also Geotextile can make by strand, ribs, and

coated ribs.

Geotextile verify in filaments. Filaments are type of fibers which are

produced by extruding molten polymer through dies or spinnerets, which

can have holes of a required diameter.

Bonding mechanism (bonding is a process confirmed during rearrange

fibers (filaments/staple fiber) over conveyor belt in continuous fashion

(lapping) to form a loose web in a nonwoven Geotextile/Geogrid fabrics.

Thus it compressed and bonded by using one or combination of the

following processes:

1. Mechanical process (needle pouching).

2. Thermal bonding (under heat and pressure).

3. Chemical bonding (using bonding agents).

Geotextile material also different in woven or non-woven patterns,

thicknesses, masses per unit area (areal density). Specific properties were

defined by ASTM and GRI.

4 FUNCTION AND APPLICATIONS

Geogrid can perform the separation, protection, and reinforcement.

Geocomposites (Geotextile/Geonet) are design to play a specific role

(mostly provide high capacity flow for drainage application).table 1 show

different functions related to their applications according to IFAI (modified

after IFAI, 1989).

5 TESTING STANDARDS FOR GEOGRID AND GEOCOMPOSITES

GEOSYNTHETICS BY ASTM AND GRI

Different type of Testing was developed relevant to their applications.

Several testing was provided use to serve industrial needs. On other hand

most civil engineering designs and applications require the Geosynthetics

materials to be tested with site-specific soils, with the testing conditions

representing those in the field. These kinds of tests are known as

performance tests. ASTM has developed standardized testing procedures

for Geogrid and Geocomposites Geosynthetics under Committee D35 for

could be listed as (related for their composite and suppose).The properties

should be tested for a specific Geosynthetics type:

1. Terminology

2. Mechanical Properties

3. Endurance Properties

4. Permeability and Filtration

5. Geosynthetics Erosion Control

6. Standards for the above listed properties are included in Appendix A

Table 1 functions related to their applications according to IFAI (modified after IFAI, 1989).

application Primary function products

Subgrade

stabilization

Separation/

Reinforcement/

Filtration

Geotextile/Geogrid

Railroad tracked

stabilization

Drainage/

Separation/

Filtration

Geotextile/Geogrid

Sedimentation

Control silt fence

Sediment retention/

Filtration/ Geotextile/Geogrid

Asphalt overlay Stress relieving layer/

Water proofing Geotextile/Geogrid

Soil reinforcement

Embankments

Steep slops

Vertical walls

Reinforcement

Geotextile/Geogrid

Erosion control filter Filtration/ Geotextile/Geogrid

Subsurface drainage

filter Filtration Geotextile/Geogrid

Geomembrance

protection

Protection

/cushion Geotextile/Geogrid

Subsurface drainage

Filtration/fluid

transmission

Prefabricated

Drainage composites

Surficial erosion

control

Turf Reinforcement

Erosion control mats

6 MECHANICALLY STABILIZED EARTH WALL

Mechanically Stabilized Earth Wall (MSEW) is a generic term that

includes reinforced soil (a term used when multiple layers of inclusions

act as reinforcement in soils placed as fill). Reinforced Earth is a

trademark for a specific reinforced soil system.

6.1 APPLICATIONS

Mechanically Stabilized Earth Walls (MSEW) is cost-effective soil-

retaining structure that can tolerate much larger settlements than

conventional reinforced concrete walls. The MSEW structures are cost-

effective alternatives for most applications where reinforced concrete or

gravity type walls have traditionally been used to retain soil. These

include bridge abutments and wing walls as well as areas where the right-

of-way (R-O-W) is restricted, such that an embankment or excavation

with stable side slopes cannot be constructed. They are particularly suited

to economical construction in steep-sided terrain, in ground subject to

slope instability, or in areas where foundation soils are poor.

There are two primary purposes for using reinforcement in engineered

slopes:

1. To increase the stability of the slope, particularly if a steeper than safe

unreinforced slope is desirable or after a failure has occurred.

2. To provide improved compaction at the edges of a slope, thus decreasing

the tendency for surface sloughing.

6.2 Advantages and Disadvantages

6.2.1 Advantages of Mechanically Stabilized Earth (MSE) Walls

MSE walls have many advantages compared with conventional reinforced

concrete and concrete gravity retaining walls. The following are the

advantages of using MSE walls:

1. Use simple and rapid construction procedures and do not require large and

heavy construction equipment.

2. Do not require experienced craftsmen with special skills for construction.

3. Require less site preparation than other alternatives.

4. Need less space in front of the structure for construction operations.

5. Reduce right-of-way acquisition.

6. Do not need rigid, unyielding foundation support because MSE structures

are tolerant to deformations.

7. Are relatively cost effective:

MSE walls are likely to be more economical than other wall systems for

walls higher than about 3 m (10 ft) or where special foundations would be

required for a conventional wall.

8. Are technically feasible to heights in excess of 25 m (80 ft).

6.2.1 The Following General Disadvantages May Be Associated With

the Soil Reinforced Structures:

1. Require a relatively large space behind the wall or outward face to obtain

enough wall width for internal and external stability.

2. MSEW require select granular fill. (At sites where there is a lack of

granular soils, the cost of importing suitable fill material may render the

system uneconomical). Requirements for RSS are typically less

restrictive.

3. Suitable design criteria are required to address corrosion of steel

reinforcing elements, deterioration of certain types of exposed facing

elements such as Geosynthetics by ultra violet rays, and potential

degradation of polymer reinforcement in the ground.

4. Since design and construction practice of all reinforced systems are still

evolving, specifications and contracting practices have not been fully

standardized, in comparison with the RSS.

5. The design of soil-reinforced systems often requires a shared design

responsibility between material suppliers and owners and greater input

from agencies geotechnical specialists in a domain often dominated by

structural engineers.

6.3 MODULAR BLOCK WALL USING FLEXIBLE GEOGRID

REINFORCEMENT

Modular block, or segmental, retaining walls employ interlocking

concrete units serve as facial material that tie-back into the earth using

Geogrid material for reinforcement. Note that the Geogrid is the structural

material for the MSE wall. These pre-engineered modular systems are an

attractive, economical, and durable alternative to stone or poured concrete

retaining walls. The inherent design flexibility can accommodate a wide

variety of site constraints, project sizes, and aesthetic preferences.

Modular block wall with low extension Geogrid is designed to provide a

required flexibility and ability to absorb deformations due to poor subsoil

conditions in the foundations. Also, based on observations in seismically

active zones, this structure has demonstrated a higher resistance to seismic

loading than have rigid concrete structures.

Modular block MSE wall will be considered as a design alternative for the

proposed project. The other design alternative is a conventional cantilever

concrete retaining wall.

Flexible Geogrid Unit block

Figure 2 Modular block wall with flexible material.

6.3.1 MSE MODULAR BLOCK WALL DESIGN FOR A RAMP

OF A BRIDGE INSTABILITY SOIL

Geotechnical evaluation of the site soils where used along with proposed

wall heights and surcharge loading to determine the extent of the

reinforcement required to construct the Modular Block retaining Wall in

addition, water table and one hundred year flood elevations were

considered during design process.

6.3.1.1 Method Statement for Construction Modular Block Wall

System with Flexible Geogrid Reinforcement

The proposed system consists machine produced concrete modular blocks

and layer of Geogrid reinforcement embedded and anchored within the

retained soil fill which will interact with surrounding soil resulting in

stabilizing the soil mass and reducing the potential for movement of the

wall in response to the vertical load being transferred horizontally as

pressure against the back of the wall. It is also required to include a

drainage system immediately behind the modular blocks in form of ¾"

single size aggregate separated from the soil fill by an adequate nonwoven

Geotextile filter.

The modular block wall system, schematically shown in figure (3)

consists of the following:

1- Leveling pad:

The leveling pad is placed under the wall facing elements to facilitate

proper alignment of facing blocks. It is commonly composed of crushed

stone (base course) or unreinforced concrete blinding.

In the event the foundation soil is weak, layer of Geogrid material could

be placed below and within the crushed soil layer.

2- Facing elements:

Is a component of the reinforced soil system used to prevent the soil from

raveling out between the rows of reinforcement. Common facings include

precast concrete panels; dry cast modular blocks, metal sheets and plates,

gabions, welded wire mesh, shotcrete, wood lagging and panels, and

wrapped sheets of Geosynthetics. The facing also plays a minor structural

role in the stability of the structure.

For this project the facing elements will compose of modular blocks (type

MB-H-20). The shape, size and the specifications for this standard block

are provided below in table 2.

Table 2 specifications for standard block

Specification Information

Size ( w x d x h ) 40 x 30 x 20 cm

Setback 10 mm per 200 mm

Weight approximate 32 kg

Cement Type used OPC

Strength 25 MPa concrete

Area 0.08 m² per block

Maximum absorption % 5

Figure 4 Block unit

3- Drainage layer:

The drainage layer is approximately 30 cm (±5 cm) wide, placed behind

the wall facing blocks. The drainage layer is separated from the reinforced

fill by a nonwoven Geotextile fabric. The drainage layer shall be

composed of ¾" single size aggregate.

Placement of well graded gravel immediately adjacent to modular blocks

is recommended for several reasons. Gravel has a high permeability that

will not impede water flow out of the reinforced mass and through the dry

stacked modular blocks. Gravel is not prone to piping through joints

between modular blocks. Gravel is also easily placed and compacted,

especially adjacent to elements such as modular blocks.

4- Reinforced fill:

Selected fill material which placed behind the wall in which the Geogrid

reinforcements layers are placed. MSE block walls require high quality

backfill for durability, good drainage, constructability, and good soil

reinforcement interaction which can be obtained from well graded and

single size granular materials. MSE systems depend on interface friction

between the reinforcing elements and the soil. In such cases, a material

with high friction characteristics is specified and required. Some systems

rely on passive pressure on reinforcing elements, and, in those cases, the

quality of backfill is still critical. These performance requirements

generally eliminate soils with high clay contents. When drainage layer is

placed behind the wall, granular fill material could be placed in reinforced

Reinforced fill proposed for this project has the following gradation:

Table 3 Reinforced fill gradation

(mm) % passing PI

< 75 mm 100 %

Max. PI = 15% Sand Fraction

(0.075 – 4.75 mm) 40 – 60%

Silt and clay

< 0.075 mm < 20%

The reinforced fill shall be placed in not exceeding 20-cm (+5cm) in

compacted thickness with a minimum relative compaction of 95% of the

maximum density obtained from laboratory measurements using standard

effort or 90% of the maximum density obtained from modified proctor.

5- Reinforcement material:

The structural reinforcements where used for this project is Flexible-

Geogrid. Flexible-Geogrid is ideal for reinforcing earth retaining support

structures. Flexible Geogrid is a woven process manufactured grid from

high-modulus, low-creep synthetic yarns and have a protective PET

polymer PVC coating. Flexible reinforcement can be supplied in various

mesh sizes and standard ultimate strength of 35 kN/m. Geogrid has a 170

kN/m² and 20 mm x 20 mm opining size.

Flexible-Geogrid is consider ideal for reinforcing earth retaining support

structures because flexible one exhibits considerably lower deformation

under permanent loading than many grids of equivalent nominal strength

from other manufactured and Transmits high tensile forces with low

elongation. Also has lower stress-strain elasticity behavior which provides

a high flexible earthen stability system resist the backfill and foundation

soil settlement.

The Geogrid and locations are to be in accordance with the designs and

finalized plans.

Figure 5 Flexible low-extension Geogrid

6- Geotextile filter:

Nonwoven Geotextile filter fabric are placed between the reinforced soil

and the drainage layer (coating each layer of reinforced soil), The

Geotextile fabric allow free drainage of water from the reinforced fill into

the granular layer while preventing the migration of fines into the

drainable soil inside the fabric.

7- Retained soil:

Is the fill material located between the mechanically stabilized soil mass

and the natural soil. This could be either soil excavated from the site

existing ground or imported fill. For this project, retained soil is the

existing soils on-site.

8- Topping, asphalt and barrier:

The pavement layer is placed on top the first layer with thickness equal to

30 cm.

Flexible post and beam barriers, when used, shall be placed at a minimum

distance of 1.0 m. (3.3 ft) from the wall face, driven 1.5 m (5 ft) below

grade, and spaced to miss the reinforcements where possible. If the

reinforcements cannot be missed, the wall shall be designed accounting

for the presence of an obstruction.

Figure 5 Section Geogrid reinforced modular block wall

6.3.1.2 INFORMATION DETAILS

Geometry

This submittal is prepared based on the received plans, the typical

geometry of the proposed wall is listed table below:

Table 4 Geometry design information

Geometry

stations

Height

from to

1 0+260 0+330 6.8 – 7.0

Single

wall with

traffic

surcharge

The proposed walls will be designed at height average equal to 7 meters,

with horizontal backfill. The facing material is to be composed of modular

blocks with inclination of 5° from the vertical.

Material properties

The properties of the reinforced fill, retained fill and foundation soils are

based on the geotechnical report prepared by others for this project and

available information. Detailing of the wall elements also specified in

statement method of construction above.

Water, boundary loads and seismicity

Water table is beyond the depth of influence. Accordingly, water will not

consider in design calculations.

Traffic load: A live traffic surcharge load of 20.0 kPa distributed was

applied to the top of the wall.

The preliminarily design incorporated seismic factor of 0.15 g.

6.3.1.3 DESIGN STANDARD AND FACTORS

The standard used for the design of this project is AASHTOO-2002/NHI-

043. This is based on allowable stress design (ASD) which is well

document and approved worldwide. The available resistances (shall

exceed the maximum calculated loads by a factor, called facto of safety

(FS). AASHTOO specified the minimum factors of safety, listed in table:

Table 5 Minimum requirement for safe design (LSD).

Item Factor of safety

(static)

Factor of safety

(seismic)

70% of static

Internal stability

pullout 1.5 1.05

Direct sliding at each

Geogrid level 1.5 1.05

Strength (Rapture) 1.5 1.05

Connection

(Geogrid-block) 1.5 1.05

External stability

Bearing capacity 2.5 1.875

Overturning e < B/6 e < B/3

Overall stability 1.5 1.125

External sliding 1.5 1.125

6.3.1.4 GEOSYNTHETICS REINFORCEMENT

The long term design strength (LTDS) of the flexible Geogrid is obtained

b applying a reduction factors o the material properties obtained from

standard laboratory testing.

The design factor of safety is applied to account for the uncertainty in the

determination if the material properties as well as the calculation and

mathematical modular error. The reduced strength is achieved by applying

these factors as shown in the following equation:

𝑇𝑑𝑒𝑠𝑖𝑔𝑛 =𝑇𝑢𝑙𝑡

𝑅𝐹𝐷 × 𝑅𝐹𝑖𝐷 × 𝑅𝐹𝑐 × 𝑅𝐹𝑐𝑛 × 𝐹𝑆

Where:

𝑇𝑑𝑒𝑠𝑖𝑔𝑛 = Maximum allowable design strength:.

𝑇𝑢𝑙𝑡 = Ultimate tensile strength.

𝑅𝐹𝐷 = Strength Reduction factor due to creep: .

𝑅𝐹𝑖𝐷 =Strength Reduction factor due to installation damage.

𝑅𝐹𝑐 = Strength Reduction factor for connection of seams .

𝑅𝐹𝑐𝑛 = Strength Reduction factor for durability.

𝐹𝑆

= Global factor of safety for design manufacture and extrapolation of data.

6.3.1.4 GEOTECHNICAL REPORT PARAMETERS

SOIL PROPERTIES:

REINFORCED SOIL PROPERTIES

Design value of internal angle of friction 𝜙𝑟

34.0°

Unit weight 𝛾𝑟 18.0 kN/m³

Cohesion 𝑐𝑟 0.0

RETAINED SOIL PROPERTIES

Design value of internal angle of friction 𝜙𝑏

32.0°

Unit weight 𝛾𝑏 18.0 kN/m³

Cohesion 𝑐𝑏 0.0

FOUNDATION SOIL PROPERTIES

Design value of internal angle of friction 𝜙𝑒

Unit weight 𝛾𝑒

18.0 kN/m³

Cohesion 𝑐𝑒

15.00 kPa

LATERAL EARTH PRESSURE COEFFICIENT:

Internal Stability

Reinforced soil earth pressure

coefficient 𝑘𝑎𝑟

Seismic inertia angle ψ

62.00°

External Stability

Retained soil earth pressure

coefficient 𝑘𝑎𝑏

Adhesive between Geogrid and

reinforced soil 𝛿

32.00°

BEARING CAPACITY:

𝑁𝑐 133.87

𝑁𝛾 271.75

𝑁𝑞 134.88

SEISMICITY:

Max. ground acceleration coefficients 𝛼° 0.15 𝑔

𝐾𝑎𝑒 𝛼° = 0.0 0.2771

𝐾𝑎𝑒 𝛼° = 0.150 0.4393

∆𝐾𝑎𝑒 = 𝐾𝑎𝑒 𝛼° = 0.150 − 𝐾𝑎𝑒 𝛼° = 0.0 0.1622

Data Base for Geogrid with Block:

Ultimate strength of Geogrid= 35.0 kN/m²

Cover ratio = 1.00

Table 6 Reduction Factors for reinforcement Geogrid

Reinforcement reduction factors

item Factor

Strength Reduction factor for

durability, 𝑹𝑭𝒅 1.03

Strength Reduction factor

installation damage, 𝑹𝑭𝒊𝑫 1.09

Strength Reduction factor creep,

𝑹𝑭𝒄 1.60

Strength Reduction factor for

connection seams, 𝑹𝑭𝒄𝒏 1.00

Reinforcement-Reinforced Soil Interaction Parameters:

Interaction parameter Factor

DIRECT SLIDING ANALYSIS FACTORS

Friction angle along Geogrid-soil

interface, ρ

PULLOUT COMPUTING FACTORS

Pullout resistance factors, F 0.9tan𝜑𝑟

Scale-effect correction factor, ∝ 1.0٭

Interaction coefficient determined

from pullout testing for a

particular reinforcement type Ci

α = 1.0 determined in laboratory specific tests performed on the٭Geogrid used.

VARIATION OF LATERAL EARTH PRESSURE COEFFICIENT

WITH DEPTH:

𝐾𝑎𝑐𝑜𝑠 𝛿 − 𝛼°

According to AASHTOO for𝛼° < 10:

𝛿 = 0.0 And 𝛼° = 0.0 is used

For all depth:

𝐾𝑎𝑐𝑜𝑠 0 − 0 = 1.0

6.3.1.5 STABILITY ANALYSIS AND FINAL DESIGN

(A) CALCULATE THE EXTERNAL STABILITY-STATIC ANALYSIS

q = 20.0 kN/m ²

ressure

Figure 6 Pressure due to the soil and surcharge load.

Retained soil lateral earth pressure coefficient:

Kab= tan² 45 −

𝐾𝑎𝑏 = 𝑡𝑎𝑛² 45 −32

2 = 0.307

Minimum Geogrid length:

𝐻 ≥ 0.7

45 +𝜑

P2 + P3

7≥ 0.7 → 𝐿 = 0.7 × 7 = 4.9 𝑚

Total Lateral load calculations

Geostatic earth load:

𝑃1 =1

2× 𝛾𝑏 × 𝐻2 × 𝐾𝑎𝑏

𝑃1 =1

2× 18 × 72 × 0.307 = 135.39

𝑘𝑁

Live load:

𝑃2 = 𝑞𝐿.𝐿𝐾𝑎𝑏 × 𝐻

𝑃2 = 20 × 0.307 × 7 = 42.98 𝑘𝑁

𝑃3 = 𝑞𝑝𝑎𝑣𝑒𝑚𝑒𝑛𝑡 𝐾𝑎𝑏 × 𝐻

𝑃3 = 0.3 22 0.307 × 7 = 14.18 𝑘𝑁

𝑃𝑎 = 𝑃𝑡𝑜𝑡𝑎𝑙 = 135.39 + 42.98 + 14.18 = 192.55 𝑘𝑁

𝑃𝑕 = 192.55𝑘𝑁

(1) Check for the sliding stability

𝐹𝑆𝑠 =𝐹

𝑃𝑕 𝐹: 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒

𝐹 = 𝑊 × 𝜇

𝜇 = tan 𝛿

𝛿 : Adhesive between bottom Geogrid layer and foundation soil

𝛿 = 32.0°

𝜇 = tan 32°

𝛾𝑟 = 18 𝑘𝑁

𝑊 = 𝛾𝑟 × 𝐻 × 𝐿

𝐹 = 18 × 7 × 4.9 × tan 32° = 385.97 𝑘𝑁

Factor of safety against sliding

𝐹𝑆𝑠 =𝐹

𝑃𝑕=

385.79

192.55= 2.00 > 1.5

Check for the overturning stability

𝐹𝑆𝒐𝒗 =𝑀𝑺

𝑀𝒐𝒗

𝑀𝑺 = 𝑊 ×𝐿

2= 617.4 ×

2= 1512.63

𝑘𝑁.𝑚

𝑀𝑜𝑣 = 𝑃1 ×𝐻

3+ 𝑃2 ×

2× 𝑃3 ×

𝑀𝑜𝑣 = 135.39 ×7

3+ 42.98 ×

2+ 14.18 ×

2= 515.97

𝑘𝑁.𝑚

Factor of safety against overturning

𝐹𝑆𝒐𝒗 =1512.63

515.97= 2.93 > 1.5

(2) Check for the bearing capacity

Check for the tension beneath the footing:

ℯ = 𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 =𝑀𝑜𝑣

∑𝑉

∑𝑉 = 𝑊 + 𝑞1 × 𝐿 + 𝑞2 × 𝐿

∑𝑉 = 617.4 + 20 × 4.9 + 6.6 × 4.9 = 747.77 𝑘𝑁

ℯ =515.97

747.77= 0.69 𝑚

ℯ <𝐿

0.69 < 0.82

(3) Check for bearing capacity

Shallow foundation bearing capacity theory:

𝑞𝑢𝑙𝑡 = 𝑐𝑁𝑐 + 𝑞𝑁𝑞 + 0.5𝛾𝐿𝑁𝛾

𝑞 = 0.0

𝑞𝑢𝑙𝑡 = 45 × 133.87 + 0.5 × 4.9 × 23.0 × 271.75 = 21337.26 𝑘𝑃𝑎

𝐴𝑐𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡𝑕 = 𝐿′ = 𝐿 − 2 ℯ

𝐿′ = 4.9 − 2 × 0.69 = 3.52 𝑚

𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑞𝑚𝑎𝑥 = [ 𝛾𝑟 × 𝐻 + 𝑞𝐿.𝐿 + 𝑞𝑝𝑎𝑣 ] × 𝐿

𝐿′

𝑞𝑚𝑎𝑥 = 18 × 7 + 20 + 6.6 × 4.9

3.52 = 212.43 𝑘𝑃𝑎

Factor of safety against bearing capacity failure:

𝐹𝑆𝑏 =21337.26

212.43= 100 ≫ 2.5

(B) CALCULATE THE INTERNAL STABILITY-STATIC ANALYSIS

𝜍𝑕 = 𝜍𝑕𝑠 + 𝜍𝑕𝑙 .𝑙 + 𝜍𝑕𝑝𝑎𝑣

Find the lateral earth pressure coefficient for reinforced soil:

𝜑𝑟 = 34°

𝐾𝑎𝑟 = 𝑡𝑎𝑛² 45 −𝜑𝑟2

𝐾𝑎𝑟 = 𝑡𝑎𝑛² 45 −34

2 = 0.283

𝜍𝑕 = 𝛾𝑟 × 𝑧 × 𝐾𝑎𝑟 + 𝑞𝐿.𝐿𝐾𝑎𝑟 + 𝑞𝑝𝑎𝑣𝐾𝑎𝑟

𝜍𝑕 = 18 × 𝑧 × 0.283 + 20 × 0.283 + 6.6 × 0.283

𝜍𝑕 = 5.094𝑧 + 7.5

(1) Find Geogrid vertical spacing

𝑇𝑑𝑒𝑠𝑖𝑔𝑛 =𝑆𝑣𝜍𝑕

𝐶𝑟

Where:

𝑆𝑣 = 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑙𝑎𝑦𝑒𝑟 𝑜𝑓 𝑔𝑒𝑜𝑔𝑟𝑖𝑑 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝐶𝑟 = 𝐶𝑜𝑣𝑒𝑟 𝑟𝑎𝑡𝑖𝑜 = 1.00

Find Maximum Allowable Design Strength:

𝑇𝑑𝑒𝑠𝑖𝑔𝑛 =𝑇𝑢𝑙𝑡

𝑅𝐹𝐷 × 𝑅𝐹𝑖𝐷 × 𝑅𝐹𝑐 × 𝑅𝐹𝑐𝑛 × 𝐹𝑆

𝑇𝑑𝑒𝑠𝑖𝑔𝑛 =35

1.03 × 1.09 × 1.60 × 1.5 × 1.0= 12.99

𝑘𝑁

Note: RFcn is equal to 1.0 because No connection seams Geogrid exist.

(2) Find Geogrid vertical spacing at depth z=7 m

𝑆𝑣 =𝐶𝑟𝑇𝑑𝑒𝑠𝑖𝑔𝑛

𝜍𝑕

Where:

𝐶𝑟 = Cover ratio

Height of the modular block unit will be consider when computing

Geogrid vertical spacing, that minimum vertical spacing is equal to that

standard height of one modular block unit (20 cm).

𝑆𝑣 =1.00 × 12.99

5.094 × 7 + 7.53= 0.30 𝑚 𝑢𝑠𝑒 0.2 𝑚 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

Spacing will consider is equal to 20 cm (equivalent to 1 Block unit height)

By try and error, check if the spacing can be opened up to 0.4 m at depth z

= 4.8 m

𝑆𝑣 =1.00 × 12.99

5.094 × 4.8 + 7.53= 0.41 𝑢𝑠𝑒 0.4 𝑚 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

By try and error, check if the spacing can be opened up to 0.60 m at depth

z = 2.4 m

𝑆𝑣 =1.00 × 12.99

5.094 × 2.4 + 7.53= 0.66 𝑢𝑠𝑒 0.60 𝑚 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

Find number of layer of compacted soil for each spacing:

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟 𝑆𝑣 = 0.2 =7 − 4.8

0.2= 11 𝑙𝑎𝑦𝑒𝑟

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟 𝑆𝑣 = 0.4 =4.8 − 2.4

0.4= 6 𝑙𝑎𝑦𝑒𝑟

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟 𝑆𝑣 = 0.6 =2.4

0.6= 4 𝑙𝑎𝑦𝑒𝑟

Now; Figure (8) show the vertical spacing between reinforcement layers.

For the embedment length:

𝑆𝑣 × 𝜍𝑕 × 𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡 = 2 × 𝐿𝑒 × 𝜍𝑣 × 𝐶𝑖tan𝜑𝑟 × 𝐶𝑟 ×∝

𝐿𝑒 =𝑆𝑣 × 𝜍𝑕 × 𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡

2 × 𝜍𝑣 × 𝐶𝑖tan𝜑𝑟 × 𝐶𝑟 ×∝

Where:

𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡 = 1.5

𝐶𝑖 = 0.9

tan𝜑𝑟 = tan 34°

∝= 1.0

No. of layer

Modular concrete block Vertical spacing 𝑆𝑣

Figure 7 vertical spacing for each layer

Geogrid

(3) Find the total length by consider the embedment length plus the non

acting rankine length

𝐿𝑒 =𝑆𝑣 5.094𝑧 + 7.53 1.5

2 × 0.9 × 18𝑧 × tan 34 × 0.8 × 1.0= 7.64𝑧 + 11.3 𝑆𝑣

17.48𝑧

For the nonacting rankine length:

𝐿𝑅 = 𝐻 − 𝑧 tan 45 −𝜑𝑟2

𝐿𝑅 = 7 − 𝑧 tan 45 −34

𝐿𝑅 = 3.72 − 0.532𝑧

Table 7 Final total length computation

LAYER NO.

DEPTH Z (m)

SPACING 𝑺𝒗 (m)

𝑳𝒆 (m)

𝑳𝒆𝒎𝒊𝒏

𝑳𝑹 (m)

𝑳𝒄𝒂𝒍𝒄 (m)

𝑳𝒓𝒆𝒒𝒅

21 0.6 0.6 0.91 1.0 3.40 4.40 5.0

20 1.2 0.6 0.59 1.0 3.08 4.08 5.0

19 1.8 0.6 0.48 1.0 2.76 3.76 5.0

18 2.4 0.6 0.42 1.0 2.44 3.44 5.0

17 2.8 0.4 0.27 1.0 2.23 3.23 5.0

16 3.2 0.4 0.26 1.0 2.02 3.02 5.0

15 3.6 0.4 0.25 1.0 1.80 2.80 5.0

14 4.0 0.4 0.24 1.0 1.59 2.59 5.0

13 4.4 0.4 0.23 1.0 1.38 2.38 5.0

12 4.8 0.4 0.23 1.0 1.17 2.17 5.0

11 5.0 0.2 0.11 1.0 1.06 2.06 5.0

10 5.2 0.2 0.11 1.0 0.95 1.95 5.0

9 5.4 0.2 0.11 1.0 0.85 1.85 5.0

8 5.6 0.2 0.11 1.0 0.74 1.74 5.0

7 5.8 0.2 0.11 1.0 0.63 1.63 5.0

6 6.0 0.2 0.11 1.0 0.52 1.52 5.0

5 6.2 0.2 0.11 1.0 0.42 1.42 5.0

4 6.4 0.2 0.11 1.0 0.32 1.32 5.0

3 6.6 0.2 0.11 1.0 0.20 1.20 5.0

2 6.8 0.2 0.11 1.0 0.10 1.10 5.0

1 7.0 0.2 0.11 1.0 0.0 1 5.0

𝑻𝒎𝒅

𝐤𝐍

𝑻𝒕𝒐𝒕𝒂𝒍

𝐤𝐍

𝑳𝒆𝒆𝒙𝒕𝒆𝒏𝒅

𝑳𝒆𝒅𝒆𝒗𝒆𝒍𝒐𝒑𝒆𝒅

𝑳𝒅𝒆𝒔𝒊𝒈𝒏

8.17 14.52 1.97 2.88 6.28

5.30 13.49 1.42 2.01 5.09

4.31 14.33 1.23 1.71 4.47

3.77 15.62 1.13 1.55 3.99

2.43 11.14 1.10 1.37 3.60

2.43 11.96 1.08 1.34 3.36

2.25 12.59 1.05 1.30 3.10

2.16 13.32 1.03 1.27 2.86

2.10 14.07 1.01 1.24 2.62

2.10 14.90 1.00 1.23 2.40

1 7.60 0.99 1.10 2.16

1 7.80 0.99 1.10 2.05

1 8.00 0.98 1.09 1.94

1 8.21 0.98 1.09 1.83

1 8.42 0.98 1.09 1.72

1 8.62 0.97 1.08 1.60

1 8.82 0.97 1.08 1.50

1 9.02 0.97 1.08 1.40

1 9.23 0.97 1.08 1.28

1 9.43 0.96 1.07 1.17

1 9.64 0.96 1.07 1.07

(C) CALCULATE THE INTERNAL STABILITY-DYNAMIC

ANALYSIS

Seismic loads produce an inertial force PI (see figure) acting horizontally,

in addition to the existing static forces.

This force will lead to incremental dynamic increases in the maximum

tensile forces in the reinforcements. It is assumed that the location and

slope of the maximum tensile force line does not change during seismic

loading.

FHWA-NHI-00-043 document recommends that the horizontal seismic

load acceleration coefficient at the center of the wall mass is taken by:

𝑘𝑕 = 𝛼° 1.45 − 𝛼°

Where:

𝑘𝑕 : Horizontal seismic load acceleration coefficient.

𝛼°: Maximum ground acceleration coefficients

𝑘𝑕 = 0.15 1.45 − 0.15 = 0.195

Find force PI per unit width acting above the base

𝑃𝐼 = 𝑘𝑕 × 𝑊𝐴

Where:

𝑃𝐼 : Inertial force due to Seismic load.

𝑊𝐴 : The weight of the active zone (shaded area on figure).

For ψ = 62.0°:

𝑊𝐴 = 𝐴𝑟𝑒𝑎 × 𝛾𝑟

𝑃𝐼 = 0.195 ×1

2× 7 × 7 × tan 28° × 18 = 45.72

𝑘𝑁

Figure 8 Weight of the active zone

Compute the Dynamic Tensile Strength:

𝑇𝑚𝑑 = 𝑃𝐼𝐿𝑒𝑖

∑ 𝐿𝑒𝑖𝑛𝑖=1

See table (7) for 𝑇𝑚𝑑 calculations for each layer

The maximum tensile force:

𝑇𝑡𝑜𝑡𝑎𝑙 = 𝑇𝑚𝑎𝑥 + 𝑇𝑚𝑑

𝑇𝑡𝑜𝑡𝑎𝑙 = 𝑆𝑣𝜍𝑕 + 𝑃𝐼𝐿𝑒𝑖

∑ 𝐿𝑒𝑖𝑛𝑖=1

At depth = 7 m

𝑇𝑡𝑜𝑡𝑎𝑙 = 𝑆𝑣 5.094𝑧 + 7.53 + 𝑃𝐼0.11

𝑇𝑡𝑜𝑡𝑎𝑙 = 0.2 5.094 × 7 + 7.53 + 1 = 9.64 𝑘𝑁

See table (7) for 𝑇𝑡𝑜𝑡𝑎𝑙 calculations for each layer.

For Geosynthetics reinforcement rupture, the reinforcement must be

designed to resist the static and dynamic component of the load as

follows:

For the static component:

𝑇𝑚𝑎𝑥 = 𝑆𝑣𝜍𝑕

𝑇𝑚𝑎𝑥 =𝑆𝑟𝑠 × 𝐶𝑟

0.7 × 𝑅𝐹 × 𝐹𝑆

Where:

𝑆𝑟𝑠 : Reinforcement strength per unit width needed to resist the static

component of load.

𝑅𝐹: Reduction factors.

For the dynamic component, where the load is applied for a short time,

creep reduction is not required and therefore:

𝑇𝑚𝑑 =𝑆𝑟𝑡 × 𝐶𝑟

0.7 × 𝑅𝐹 × 𝐹𝑆

Where:

𝑆𝑟𝑡 : Reinforcement strength needed to resist the dynamic or transient

component of load.

For the total pullout under seismic loading, for all reinforcements, the

friction coefficient F* should be reduced to 100 % percent of the static

value, leading to

𝑃𝑟𝑒𝑑 =𝑆𝑟𝑠 + 𝑆𝑟𝑡

𝑅𝐹

𝑇𝑡𝑜𝑡𝑎𝑙 =𝑃𝑟𝑒𝑑×𝐶𝑟

0.7 × 𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡

𝑇𝑡𝑜𝑡𝑎𝑙 =2 × 1.0 × 𝐹∗ × 𝑆𝑣𝜍𝑕 × 𝐿𝑒𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 × 𝐶𝑟

0.7 × 𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡

𝐹𝑆𝑝𝑢𝑙𝑙𝑜𝑢𝑡 = 1.5

𝐿𝑒𝑒𝑥𝑡𝑒𝑛𝑑 =0.7 × 1.5 × 𝑇𝑡𝑜𝑡𝑎𝑙

2 × 1.0 × 0.9 tan 34 × 𝑆𝑣 5.094𝑧 + 7.53 × 1.0

At depth = 7 m

𝐿𝑒𝑒𝑥𝑡𝑒𝑛𝑑 =0.7 × 1.5 × 9.64

2 × 1.0 × 0.9 tan 34 × 0.2 5.094 × 7 + 7.53 × 1= 0.695 𝑚

See table (7) for𝐿𝑒𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 for each layer.

6.3.1.6 CONNECTION STRENGTH BETWEEN

GEOSYNTHETICS REINFORCEMENT AND MODULAR BLOCK

For the connection strength theoretically the tensile stress at the

connection of the reinforcements to the modular block units is must to

checked this is indeed the case of unit block, reinforcement , and soil

backfill stay in horizontal alignment in the same manner as this

constructed.

Settlement of the backfill and perhaps of the foundation soil usually

occurs, thereby deforming the reinforcement and imposing stresses which

effect interaction between the internal face of the block units and

reinforcement .the amount of this stresses is depend on the backfill soil

type, density, moisture content, compactive effort and foundation

condition.

Determining Connection strength between Geosynthetics reinforcement

and modular block unit:

MSE walls constructed with MBW units are connected either by a

structural connection subject to verification under AASHTO Article 8.31

or by friction between the units and the reinforcement, including the

friction developed from the aggregate contained within the core of the

units or by a combination of friction and shear from connection devices.

This strength will vary with each unit depending on its geometry, unit

batter, normal pressure and depth of unit. The connection strength is

therefore specific to each unit/reinforcement combination and must be

developed uniquely by test for each combination.

ASTM provides a method to indicate the connection strength between

Geosynthetics reinforcement and modular block unit.

ASTM D 6638-06 is a recommended test use to indicate the ultimate

strength provides by unit block weights to prevent the failure occurs due

to pullout force induced and probability breaking failure of the

reinforcement material is some cases.

ASTM D 6638-06 STANDARD PARAMETER AND RESULTS:

Test parameter

Test direction MD (machine direction)

Tensile strength 35.0

Dimension of single(L X W X H) 30 x 40 x20 cm

Weight of single 38.9 kg

Strands per meter 44.2

Specimen width (strands) 43

Connectors Friction

Pullout speed 40 mm/min

Granular fill Crushed gravel 8/16

Temperature 21° C

Humidity 50 %

Displacement measuring device Rope displacement gauge

RESULTS:

Load Stages

Normal Load kN/m

Equivalent Wall

height m

Peak connection capacity 𝑇𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛

Test 2nd

Test 3rd

1 3.5 0.6 8.7 - -

2 10.5 1.8 15.9 - -

3 17.5 3.0 15.8 16.2 17.8

4 24.5 4.2 18.0 - -

5 33.8 5.8 18.1 - -

A relatively conservative approach is to use the design strength of the

reinforcement material as the required connection strength. For our

project:

𝑇𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 ≥ 1.0𝑇𝑑𝑒𝑠𝑖𝑔𝑛

7 CONVENTIONAL CANTILEVER CONCRETE RETAINING

WALL DEIGNS APPROACH

The other solution for the instability soil is the reinforced concrete

retaining wall which is the commonly method and widely used in

geotechnical field. The next design approach will describe the Design

details of the imposed cantilever retaining wall.

7.1 STABILITY ANALYSIS AND DESIGN DETAILS OF 7 m

HEIGHT CANTILEVER RETAINING WALL SYSTEM.

GENERAL CONSIDRATIONS

Note: All geometery shown in Figure A

hight wall average (H) = 7.0 m

Assume D = 1.5 m > 0.6 m

H' = H + D = 7.0 + 1.5 = 8.5 m

D - 0.1 8.5 = 1.5 - 0.85 = 0.65 m

H = 7 + 0.65 = 7.65 m

H = 0.1 8.5 = 0.85 m

RANKINE ACTIVE FORCE PER UNIT LENGTH

total soil L.L pav

a a + a + a

φ = 34.0°

kNγ = 18.0

m²α = 0.0

P = P P P

1P = γ H'²K

φK = tan² 45 -

K = tan² 45 - = 0.2832

8585 340

Figure 9 Geometries information of retaining wall.

20.0 kPa

Pavement

layer layer

Force due to the soil:

P = 18 8.5 ² 0.283 = 184 2 m

Live load calculations:

L.L L.L

pav pav

pav asphalt pav

total h

soil pav L.L

P = q K H'

kNP = 20 0.283 8.5 = 48.11

P = q K H'

kNq = γ H = (22)(0.3) = 6.6

P = 6.6 0.283 8.5 = 15.9 m

kNP = P = 184 + 48.11 + 15.9 = 248

mP = P sin + P + P

P = 0 + 20 3. kN

4 22 0.3 3.4 90.44 m

Factor of safety against overturning

Moment kN.m

Moment arm from

point C m

Weight/unit length kN/m

Area m²

Section No.

130.78 1.45 90.194 (0.5)(7.65) = 3.825 1

34.20 1.08 31.57 (0.5)(0.35)(7.65)=

1.34 2

260.66 2.55 102.22 (0.85)(5.1) = 4.34 3

1591.81 3.4 468.18 (3.4)(7.65) = 26.01 4

231 3.4 (20)(3.4)=68 - 5

76.30 3.4 (22)(0.3)(3.4)=22.44 - 6

∑MR = 2324.75

∑V = 782.6

γ Concrete = 23.58 kNlm³

soil L.L pavo a a a

Roverturning

H' H'H'M = P + P + P3 2 2

8.5 8.5 8.5 kN.m= 184 + 48.11 + 15.9 = 793.38

3 2 2 m

M 2324.75FS = = = 2.93 < 1.5

M 793.38

BCheck for e <

net R o

( minimum requirment for LSD )

kN.mM = M - M = 2324.75 - 793.38 = 1531.4

mM 1531.4

X = = = 1.957 mV 782.6

B 5.1e = - X = - 1.957 = 0.593

e < = 0.856

Factor of safety against sliding

p p 2 2 p

2 2 psliding

sliding

δ = 0.95φ

δ = 0.95 34° = 32°

D = 1.5 m

φK = tan² 45 +

45K = tan² 45 + = 5.828

1P = K γ D² + 2c K D

P = 5.828 23 1.5 ² + 2 15 5.828 1.52

kN = 259.44

V tanδ + Bk c + PFS =

Pk = 0.95

782.6 tan32° + 5.1FS =

0.95 15 + 259.44= 3.3 > 1.5

Factor of safety against bearing capacity

max toe

heel min

V 6e 782.6 6 x0.593q = q = 1 ± = 1 + = 260.5

B B 5.1 5.1

782.6 6x0.593 q = q = 1 - = 46.4

5.1 5.1

φ = 45.0°

γ = 23.0

q = γ D = 23.0 1.5 = 34.5

B' = B - 2e = 5.1 - 2 0.593 = 3.914

D 1.5F = 1 + 0.4 = 1 + 0.4 = 1.

B' 3.914

qd 2 2

DF = 1 + 2 tan φ 1 - sin φ ²

= 1 + 2 tan 45° 1 - sin 45° ² = 1.0663.914

P cos α 248.0ψ = tan -¹ = tan -¹ = 17.58°

åV 782.6

ψ° 17.58°F = F = 1 - = 1 - ² = 0.647

90° 90°

Fγ = 1

ubearing capacity

ψ° 17.58°F = 1 - ² = 1 - ² = 0.371

φ ° 45.0°

q = 15 133.88 1.154 0.647 + 34.5 134.88 1.066 0.647

1+ 23 3.914 271.76 1 0.371 = 9246.97

q 9246.97FS = = = 35.5 >> 3

q 260.5

bearing capacity

FS > 2.5 ( minimum requirment for LSD )

STEM DESIGN

𝜍𝑕 = 𝛾1𝑧 + 𝑞𝑝𝑎𝑣 + 𝑞𝐿.𝐿 𝐾𝑎

𝑃𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 = 1

2𝛾1𝑧

2 + 𝑞𝑝𝑎𝑣 𝑧 + 𝑞𝑝𝑎𝑣 𝑧 𝐾𝑎

𝑀 = 𝑃 × 𝑎𝑟𝑚 = 𝑧

2𝛾1𝑧

2 + 𝑧

2 𝑞𝑝𝑎𝑣 𝑧 +

2 𝑞𝐿 .𝐿𝑧 𝐾𝑎

𝑀 = 1

6𝛾1𝑧

2𝑞𝑝𝑎𝑣 𝑧

2𝑞𝐿.𝐿𝑧

2 𝐾𝑎

Find Mu (Ultimate design moment):

ACI Code Appendix C9.2.3 defined required factored load for structures

resist due to pressure o soil should be not less:

𝑀𝑢 = 1.7𝑀

𝑀𝑢 = 1.7 1

6𝛾1𝑧

2𝑞𝐿.𝐿𝑧

2 𝐾𝑎 equ. A

𝐴𝑠 =0.85𝑓′𝑐𝑎𝑏

𝑓𝑦=

0.85 × 27.58 × 𝑎 × 1

413.7= 0.0567𝑎 equ. B

𝑀𝑢 = ∅𝐴𝑠𝑓𝑦 𝑑 −𝑎

𝜙 = 0.9

𝑀𝑢 = 0.9 × 0.0567𝑎 × 413.7 × 103𝑘𝑁

𝑚2 × 𝑑 −𝑎

𝑀𝑢 = 21111.11𝑎𝑑 − 10555.56𝑎2 equ. C

Thickness of stem

𝑴𝒖 (kN.m/m)

𝑨𝒔 (cm²)

0 0.5 0.42 0 0 0

1.53 0.57 0.49 20.15 0.0019 1.08

3.06 0.64 0.56 101.27 0.0086 4.88

4.56 0.71 0.63 269.90 0.0206 11.68

6.12 0.78 0.7 570.49 0.0397 22.51

7.65 0.85 0.77 1020.63 0.0656 37.19

d=thickness of stem – 0.08 m

𝑴𝒖 from equation (A)

a from equation(C)

𝑨𝒔 from equation(B)

Note: for 𝑨𝒔 < 𝑨𝒔 𝒎𝒊𝒏 use 𝑨𝒔 𝒎𝒊𝒏 = 𝟏𝟐.𝟕𝟓 cm²

𝐴𝑆 𝑚𝑖𝑛 ACCORDING ACI CODE SEC. 14.3.2:

𝐴𝑆 𝑚𝑖𝑛 = 0.0015 × 𝑔𝑟𝑜𝑠𝑠 𝑤𝑎𝑙𝑙 𝑎𝑟𝑒𝑎

𝐴𝑆 𝑚𝑖𝑛 = 0.0015 × 1.0 × 0.85 = 12.75 𝑐𝑚2

Reinforcement of Stem:

Try bars of 25-mm diameter and 8 bars:

𝐴𝑆 = 8 × 𝜋 × 25

× 10−2 = 39.25 𝑐𝑚2 = 0.003925 𝑚²

𝑠𝑝𝑎𝑐𝑖𝑛𝑔 =1000 ×

× 252 × 10−6

0.003925= 125.1 𝑐𝑚

Use spacing of 120 cm c/c

𝑎 =𝐴𝑆

0.0561=

39.25 × 10−4 𝑚

0.0567= 0.0692 𝑚

𝑀𝑢 = 21111.11 × 0.0692𝑑 − 10555.56 × 0.06922

𝑀𝑢 = 1460.88𝑑 − 50.55

For 𝐴𝑆 𝑚𝑖𝑛 :

Try bars of 20-mm diameter and 4 bars:

𝐴𝑆 = 4 × 𝜋 × 20

× 10−2 = 15.70 𝑐𝑚2

× 202 × 10−6

0.00157= 200.10 𝑐𝑚

Use spacing of 200 mm c/c

𝑎 =𝐴𝑆

0.0567=

15.70 × 10−4 𝑚

0.0567= 0.0280 𝑚

𝑀𝑢 = 21111.11 × 0.0280𝑑 − 10555.56 × 0.02802

𝑀𝑢 = 591.11𝑑 − 8.28 equ. D

For lapping of 20-mm diameter bars to the 25-mm diameter bars refer to

ACI Code Section 12.15 and because 100% of the bars are to lapped, the

lap splice class is B:

ℓ𝑑 = 𝑓𝑦×𝛹𝑒×𝛹𝑡

1.7𝜆 𝑓 ′ 𝑐 𝑑𝑝

ℓ𝑑 =413.7 × 1 × 1

1.7 × 1 × 27.58= 1185.5 𝑚𝑚

ℓ𝑑 = 1185.5 𝑚𝑚 ≅ 1.186 𝑚

𝑙𝑎𝑝 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 1.3 × 1.186 = 1.542 𝑚

Cutoff point indicated by combining equations (equ.A) and (equ.D):

6𝛾1𝑧

2𝑞𝐿.𝐿𝑧

2 𝐾𝑎 = 591.11𝑑 − 8.28

Where 𝑑 = 0.046𝑧 + 0.42

6(18)𝑧3 +

2 6.6 𝑧2 +

2(20)𝑧2 0.283 = 591.11 0.046𝑧 + 0.42 − 8.28

𝑧 = 5.23 𝑚

The extend of 25-mm diameter bars above the base of the stem is equal

7.65 − 5.23 + 1.542 = 3.96 𝑚

d at z= (3.69 m)

𝑑 = 0.046 × 3.69 + 0.42 = 0.590

0.17𝜙 𝑓 ′ 𝑐𝑏𝑑 = 0.17 0.75 27.58 0.590 = 0.3951 𝑀𝑁

= 395.1 𝑘𝑁

395.1 × 23 = 263.4 𝑘𝑁

𝑉𝑢 = 1.7 × 1

2× 18 × 3.692 + 20 × 2.04 + 6.6 × 2.04 × 0.283 = 106.18 𝑘𝑁

𝑉𝑢 = 106.18 𝑘𝑁 < 270.11 𝑘𝑁

Determining the development length of the main reinforcement bars into

the foundation:

According to ACI Code sec. 12.2.2:

𝑙𝑑 = 1186 𝑚𝑚

But 𝑙𝑑 > 0.85 𝑚, so:

Obtain the development length in tension using standard hooks:

Tensile stress of a standard development hook:

𝑓𝑕 = 𝑥 𝑓 ′ 𝑐

X for 25 mm equal 30

𝑓𝑕 = 30 27.58 = 157.55 𝑀𝑃𝑎

The remaining stress to be developed is:

𝑓𝑦 − 157.55 = 413.7 − 157.55 = 256.15 𝑀𝑃𝑎

The extra embedment length required to develop the stress of 256.15 is:

256.15

𝑓𝑦× 𝑙𝑑 =

256.15

413.7× 1186 = 734.3 𝑚𝑚 ≅ 0.73 𝑚

For cover 75 mm:

The minimum thickness of the base slab to the bottom of the hook:

0.73 + 3 × 0.025 + 0.075 = 0.88 𝑚

Where (3 x 0.025) is the radius of standard hook.

Use base of thickness = 0.9 m

Shear strength at the base of the wall:

𝑉𝑢 = 1.7 × 1

2× 18 × 7.652 + 20 × 7.65 + 6.6 × 7.65 × 0.283 = 351.29

𝑘𝑁.𝑚

Shear key of 50 mm x 100 mm is used at the base of stem:

𝑉𝑢𝐴𝑘𝑒𝑦

< 0.2𝜙𝑓 ′ 𝑐

Where 0.2𝜙𝑓 ′𝑐is the nominal stress.

351.29

0.1 × 1< 0.2 × 0.75 × 27.58

3512.9 𝑘𝑁 𝑚2 < 4.137 𝑀𝑃𝑎 = 4137 𝑘𝑁 𝑚2

Temperature and Shrinkage Steel:

According ACI Code sec. 14.3.3(horizontal temperature and Shrinkage

Steel):

𝐴𝑠 = 0.0025 × 1 × 0.85 = 2.125 × 10−3 𝑚2

𝑚= 21.25

𝑐𝑚2

Where 1 × 0.85 is the gross wall area.

× 182 × 10−6

2.125 × 10−3 = 119.689 𝑐𝑚

Use 18-mm diameter bars with spacing of 120 mm c/c

HEEL DESIGN

Thickness of slab= 0.9 m

𝑞 = 𝛾𝐻1 + 𝛾𝑐 0.9 − 𝑞𝑕𝑒𝑒𝑙 + 𝑚𝑥

𝑚 =𝑞𝑡𝑜𝑒 − 𝑞𝑕𝑒𝑒𝑙

260.5 − 46.4

5.1= 42

Critical section for toe and heel

m = 421

𝑞𝑚𝑎𝑥 x' x 𝑞𝑚𝑖𝑛

Figure 10 Design of heel and toe of retaining wall

𝑞 = 18 × 7.65 + 23.58 × 0.9 − 46.4 − 42𝑥 = 112.5 − 42𝑥

𝑉 = 𝑞𝑑𝑥 = 112.5𝑥 −42𝑥2

2+ 𝐶

At x = 0, V = 𝐶 = 𝑃𝑣 =90.44 𝑘𝑁

𝑉 = 112.5𝑥 −42𝑥2

2+ 90.44

𝑀 = 𝑉 𝑑𝑥 =112.5𝑥2

42𝑥3

6+ 90.44𝑥

V ultimate at x = 3.4 m (critical section):

𝑉 = 230.18 𝑘𝑁

𝑉𝑢 = 1.7 × 447.24 = 391.31 𝑘𝑁

M ultimate at x = 3.4 m:

𝑀 = 682.62 𝑘𝑁.𝑚

𝑀𝑢 = 1.7 × 682.62 = 1160.45 𝑘𝑁.𝑚

Check for shear:

b = 1, d = 0.9 – 0.075 – 0.025/2 = 0.813 m

𝑉𝑐 = 0.17 × 27.58 × 0.813 = 0.725 𝑀𝑁

𝜙𝑉𝑐 = 0.75 × 0.725 = 0.5438 𝑀𝑁

𝑚= 543.8

𝑘𝑁

𝜙𝑉𝑐 > 𝑉𝑢 = 391.31 𝑘𝑁

Flexural reinforcement:

2 = 1160.45

𝑘𝑁.𝑚

𝐴𝑠 = 0.0567𝑎

1160.45 = 0.9 × 0.0567𝑎 × 413.7 × 103 × 0.813 −𝑎

𝑎 = 0.0707

𝐴𝑠 = 0.0567 × 0.0707 = 0.00401 𝑚2 = 40.1 𝑐𝑚2

𝜌 =𝐴𝑠𝑏𝑑

=0.00401

1 × 0.813= 0.00493

𝑠𝑝𝑎𝑐𝑖𝑛𝑔 =1000 × 𝜋 × 12.52 × 10−6

0.00401= 122.41 𝑐𝑚

Use spacing of 120 mm c/c

This will provide:

𝐴𝑠 =1000

4 2.5 2 = 40.88 𝑐𝑚2

TOE DESIGN

𝑞 = −𝛾𝑐 0.9 + 𝑞𝑡𝑜𝑒 −𝑚𝑥′

𝑞 = −23.58 × 0.9 + 260.5 − 42𝑥′ = 239.28 − 42𝑥′

𝑉 = 𝑞 𝑑𝑥′ = 239.28𝑥′ −42𝑥′2

𝑀 = 𝑉 𝑑𝑥′ =239.28𝑥′2

42𝑥′3

For the critical section (x’ = 0.85 m):

𝑉 = 188.22

𝑉𝑢 = 1.7 × 188.22 = 319.97

𝑀 = 82.14

𝑀𝑢 = 139.64

Check for shear:

Because the ultimate shear at the critical section of the toe is less than

ultimate shear of the critical section of the heel the section is adequate for

shear.

Flexural reinforcement:

2 = 1160.45

𝑘𝑁.𝑚

𝐴𝑠 = 0.0567𝑎

139.64 = 0.9 × 0.0567𝑎 × 413.7 × 103 × 0.813 −𝑎

𝑎 = 0.00818

𝐴𝑠 = 0.0567𝑎 = 0.0567 × 0.00818 = 0.000464 𝑚2

𝜌 =𝐴𝑠𝑏𝑑

=0.000464

1 × 0.813= 0.000571 < 𝜌𝑚𝑖𝑛

𝐴𝑠𝑚𝑖𝑛 = 𝜌𝑚𝑖𝑛 𝑏𝑡 = 0.0018 × 1 × 0.9 = 0.00162 𝑚2 = 16.2 𝑐𝑚2

Hence provide 25-mm diameter bars at 300 mm center to center whish

𝐴𝑠 =1000

4 2.5 2 = 16.35 𝑐𝑚2

Shrinkage and Temperature Reinforcement for Heel and Toe:

For Shrinkage at and temperature reinforcement minimum steel shall be

𝐴𝑠𝑚𝑖𝑛 = 𝜌𝑚𝑖𝑛 𝑏𝑡 = 0.0018 × 1 × 0.9 = 0.00162 𝑚2 = 16.2 𝑐𝑚2

Provide 18-mm diameter bars at 150 mm center to center:

𝐴𝑠 =1000

4 1.8 2 = 16.96 𝑐𝑚2

Final design sketch of the retaining wall is shown in figure (12)

Top of the base slab 𝑑𝑝 = 25 mm

Standard hook

12 𝑑𝑝 = 300 mm Rad = 3 × 𝑑𝑝 = 750 𝑚𝑚

Figure 11 standard hook details

18 mm bars at 120 c/c 20 mm bars at 200 c/c

14 mm bars at 250 c/c 25 mm bars at 120 c/c

34085 85

50 x 100 m 18 mm bars at 150 c/c Shear key 25 mm bars at 120

Standard hook 25 mm bars at 300 c/c

150 mm hook

All geometries shown are in cm.

The concrete cover thickness is:

75 mm for flexure.

80 mm for tension (stem reinforcement)

Figure 12 Final design sketch of the retaining wall

Appendix A

Testing standards for Geogrid and Geocomposites Geosynthetics by ASTM and

Terminology

D4439-00 Standard Terminology for Geosynthetics

Mechanical Properties

D4354-99 Standard Practice for Sampling of Geosynthetics for Testing

D4595-86(1994) Standard Test Method for Tensile Properties of

Geotextiles by the Wide-Width Strip Method

D4759-88(1996) Standard Practice for Determining the Specification

Conformance of Geosynthetics

D5261-92(1996) Standard Test Method for Measuring Mass per Unit Area

of Geotextiles

D5321-92(1997) Standard Test Method for Determining the Coefficient of

Soil and Geosynthetic or Geosynthetic and Geosynthetic Friction by the Direct

Shear Method

D6364-99 Standard Test Method for Determining the Short-Term

Compression Behavior of Geosynthetics

D6637-01 Standard Test Method for Determining Tensile Properties of

Geogrids by the Single or Multi-Rib Tensile Method

Endurance Properties

D1987-95 Standard Test Method for Biological Clogging of Geotextile or

Soil/Geotextile Filters

D4594-96 Standard Test Method for Effects of Temperature on Stability of

Geotextiles

D5262-97 Standard Test Method for Evaluating the Unconfined Tension

Creep Behavior of Geosynthetics

D5322-98 Standard Practice for Immersion Procedures for Evaluating the

Chemical Resistance of Geosynthetics to Liquids

14 Ling

D5496-98 Standard Practice for In-Field Immersion Testing of

Geosynthetics

D5596-94 Standard Test Method for Microscopic Evaluation of the

Dispersion of Carbon Black in Polyolefin Geosynthetics

D5819-99 Standard Guide for Selecting Test Methods for Experimental

Evaluation of Geosynthetic Durability

D5885-97 Standard Test Method for Oxidative Induction Time

of Polyolefin Geosynthetics by High-Pressure Differential Scanning

Calorimetry

D5970-96 Standard Practice for Deterioration of Geotextiles from Outdoor

Exposure

D6213-97 Standard Practice for Tests to Evaluate the Chemical Resistance

of Geogrids to Liquids

of Geonets to Liquids

of Geotextiles to Liquids

Permeability and Filtration

D4491-99a Standard Test Methods for Water Permeability of Geotextiles by

Permittivity

D4716-00 Standard Test Method for Determining the (In-Plane) Flow Rate

per Unit Width and Hydraulic Transmissivity of a Geosynthetic Using a Constant

D4751-99a Standard Test Method for Determining Apparent Opening Size

of a Geotextile

D5141-96(1999) Standard Test Method for Determining Filtering

Efficiency and Flow Rate of a Geotextile for Silt Fence Application Using

Site-Specific Soil Civil Applications of Geosynthetics 15

D5199-01 Standard Test Method for Measuring the Nominal Thickness of

Geosynthetics

D5493-93 (1998) Standard Test Method for Permittivity of Geotextiles

Under Load

D5567-94(1999) Standard Test method for Hydraulic Conductivity Ratio

(HCR) Testing of Soil/Geotextile Systems

D6088-97 Standard Practice for Installation of Geocomposite Pavement

Drains

D6140-00 Standard Test Method to Determine Asphalt Retention of Paving

Fabrics Used in Asphalt Paving for Full-Width Applications

D6523-00 Standard Guide for Evaluation and Selection of Alternative

Daily Covers (ADCs) for Sanitary Landfills

D6574-00 Test Method for Determining the (In-Plane) Hydraulic Transmissivity of a Geosynthetic

Appendix B

References

ASTM, standard on Geosynthetics, 5th ed. Philadelphia, PA: ASTM,

2000. JP Giroud. Geosynthetics Bibliolography. Vols.1 & 2. St. Paul.

MN: international fabric Assoc. international, 1993.

Hoe 1. Ling Dov leshchinsky, Fumio Tatsuoka. Reinforced soil

engineering. Edition 1, editor, Michael D. Meyer, Library of congress.

David I. Cook. GEOSYNTHETICS, Editor, Dr. Sally Humphreys. P-32,

R.D. Holtz, Ph.D., P.E., Barry R. Christopher, Ph.D., Ryan r .berg, P.E.

Geosynthetics design and construction guidelines. Edition 1, 1998.

G Venkattapa reo, G V suryanarayana Raju. Engineering with

GEOSYNTHETICS. First reprint. Tata McGraw-hill. 1996.

GEOSYNTHETICS FOR SOIL REINFORCEMENT, 2001. P.D. Holtz,

Ph.D.R.(Report)

Dr. A. K. Haghi. Experimental analysis of Geotextile and geofibers

composites. Bub: WSEAS Press.

Robert M. Cornoer.Designing with Geosynthetics, Bub. Prentice Hall; 5

edition (April 24, 2005)

Mechanically Stabilized Earth Walls (MSE) and Reinforced Soil Slopes

(RSS), Design and Construction Guidelines Manual, by FHWA SA-96-

071, NHI – National Highway Institute.

TBU (Institut für textile Bau- und Umwelttechnik GmbH), results ASTM

D 6638-06 test report provider.

Hueshker Synthetics GmbH (engineering with Geosynthetics),

geotechnical report parameters, material reinforcement and modular block

information details and properties provider.

Design and Construction Monitoring of Mechanically Stabilized Earth

Structures, by J.A. DiMaggio, FHWA, March 1994.

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